The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected; and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. the first six books, together with the eleventh and twelfth |
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Seite 232
Sec N. SOM OLID parallelepipeds which are upon equal bases , and of the same altitude , are equal to one another . Let the solid parallelepipeds AE , CF , be upon equal bases AB , CD , and be of the same altitude ; the solid AE is equal ...
Sec N. SOM OLID parallelepipeds which are upon equal bases , and of the same altitude , are equal to one another . Let the solid parallelepipeds AE , CF , be upon equal bases AB , CD , and be of the same altitude ; the solid AE is equal ...
Seite 233
But let the solid parallelepipeds SE , CF be upon equal bases SB , CD , and be of the same altitude , and let their insisting straight lines be at right angles to the bases ; and place the bases SB , CD in the same plane , so that CL ...
But let the solid parallelepipeds SE , CF be upon equal bases SB , CD , and be of the same altitude , and let their insisting straight lines be at right angles to the bases ; and place the bases SB , CD in the same plane , so that CL ...
Seite 234
... PS , and of the same altitude , and have their insisting straight lines at right angles to to the bases : And the solid EQ is equal 234 THE ELEMENTS.
... PS , and of the same altitude , and have their insisting straight lines at right angles to to the bases : And the solid EQ is equal 234 THE ELEMENTS.
Seite 235
SOLOT OLID parallelepipeds which have the fame altitude , See N. are to one another as their bases . Let AB , CD be folid parallelepipeds of the same altitude : They are to one another as their bases ; that is , as the base AE to the ...
SOLOT OLID parallelepipeds which have the fame altitude , See N. are to one another as their bases . Let AB , CD be folid parallelepipeds of the same altitude : They are to one another as their bases ; that is , as the base AE to the ...
Seite 238
... EAS , are of the fame altitude . Therefore the solid AB B 32. II . is to the solid AY , as b the base AE to the base AS ; that is , as the straight line a is to c . And the folid AY is to the solid a B G D L K Y N E P M а .
... EAS , are of the fame altitude . Therefore the solid AB B 32. II . is to the solid AY , as b the base AE to the base AS ; that is , as the straight line a is to c . And the folid AY is to the solid a B G D L K Y N E P M а .
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added alſo altitude angle ABC angle BAC baſe becauſe Book Book XI caſe circle circle ABCD circumference common cone cylinder definition demonſtrated deſcribed diameter divided double draw drawn equal equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane produced prop proportionals propoſition pyramid radius reaſon rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid angle ſphere ſquare ſquare of AC Take taken theſe third triangle ABC wherefore whole
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Seite 32 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Seite 165 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF.
Seite 170 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 10 - When several angles are at one point B, any ' one of them is expressed by three letters, of which ' the letter that is at the vertex of the angle, that is, at ' the point in which the straight lines that contain the ' angle meet one another, is put between the other two ' letters, and one of these two is...
Seite 55 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Seite 32 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.
Seite 45 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 211 - AB shall be at right angles to the plane CK. Let any plane DE pass through AB, and let CE be the common section of the planes DE, CK ; take any point F in CE, from which draw FG in the plane DE at right D angles to CE ; and because AB is , perpendicular to the plane CK, therefore it is also perpendicular to every straight line in that plane meeting it (3.
Seite 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 304 - Thus, if B be the extremity of the line AB, or the common extremity of the two lines AB, KB, this extremity is called a point, and has no length : For if it have any, this length must either be part of the length of the line AB, or of the line KB.
Bibliografische Informationen
| Titel | The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected; and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. the first six books, together with the eleventh and twelfth |
| Autor/in | Robert Simson |
| Verlag | J. Nourse, London, and J. Balfour, Edinburgh, 1775 |
| Original von | University of Michigan |
| Digitalisiert | 11. Juni 2007 |
| Länge | 520 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |